The Atlantic Meridional Overturning Circulation (AMOC) is an important component of the global climate, known to be a tipping element, as it could collapse under global warming. The main objective of this study is to compute the probability that the AMOC collapses within a specified time window, using a rare-event algorithm called Trajectory-Adaptive Multilevel Splitting (TAMS). However, the efficiency and accuracy of TAMS depend on the choice of the score function. Although the definition of the optimal score function, called ``committor function" is known, it is impossible in general to compute it a priori. Here, we combine TAMS with a Next-Generation Reservoir Computing technique that estimates the committor function from the data generated by the rare-event algorithm. We test this technique in a stochastic box model of the AMOC for which two types of transition exist, the so-called F(ast)-transitions and S(low)-transitions. Results for the F-transtions compare favorably with those in the literature where a physically-informed score function was used. We show that coupling a rare-event algorithm with machine learning allows for a correct estimation of transition probabilities, transition times, and even transition paths for a wide range of model parameters. We then extend these results to the more difficult problem of S-transitions in the same model. In both cases of F-transitions and S-transitions, we also show how the Next-Generation Reservoir Computing technique can be interpreted to retrieve an analytical estimate of the committor function.

翻译：大西洋经向翻转环流（AMOC）是全球气候系统的重要组成部分，已知为气候临界要素，可能在全球变暖背景下发生崩溃。本研究的主要目标是通过一种名为轨迹自适应多级分裂（TAMS）的罕见事件算法，计算AMOC在特定时间窗口内崩溃的概率。然而，TAMS的效率和精度取决于评分函数的选择。尽管被称为“承诺函数”的最优评分函数在定义上已知，但通常无法先验计算。本研究将TAMS与下一代储层计算技术相结合，利用罕见事件算法生成的数据估计承诺函数。我们在AMOC的随机箱模型中测试该技术，该模型存在两种转变类型：快速转变与慢速转变。快速转变的计算结果与文献中使用物理信息评分函数所得结果高度吻合。研究表明，将罕见事件算法与机器学习相结合，能够准确估计多种模型参数下的转变概率、转变时间乃至转变路径。我们进一步将结果拓展至同一模型中更具挑战性的慢速转变问题。针对快速转变与慢速转变两种情况，我们还展示了如何通过解析下一代储层计算技术的结果，获得承诺函数的解析估计。